7x+2/x-3=9

Solution for 7x+2/x-3=9 equation:

7x+2/x-3=9

We move all terms to the left:

7x+2/x-3-(9)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x+2/x-12=0

We multiply all the terms by the denominator


7x*x-12*x+2=0

We add all the numbers together, and all the variables

-12x+7x*x+2=0

Wy multiply elements

7x^2-12x+2=0

a = 7; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·7·2
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{22}}{2*7}=\frac{12-2\sqrt{22}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{22}}{2*7}=\frac{12+2\sqrt{22}}{14}
$